My starting point is (not surprisingly) the characteristics that Dworkin and Oberon exhibit separately or eccentrically from their descendants. It might be fair to say that Dworkin and Oberon are not well understood by the Royals of Amber. It might also be clear that Oberon and Dworkin seem to prefer it this way. You might further suppose that they've gone to a lot of trouble down through the centuries to make sure they are not understood well, to take extra steps to obscure the truth wherever possible.
Why would that be?
I assumed this might be an intrinsic element of their Chaos culture, but then why wouldn't the kids pick it up as strongly? We do see that the royals only tell as much as they have to as it suits their own positions, but this manner isn't nearly held as bizarrely rigid as Dworkin and Oberon hold their secrets. The difference?
Perhaps there are many explanations, I chose this one: Oberon and Dworkin are secretive and closed mouth by rote and drill. They exhibit the cautions of their earliest catechism. These are properties imprinted into them by a harsh and demanding system; a rigid system of tradition honed by success. There is the wrong way and there are the ways of Chaos. But Oberon does not use this "perfect system" on his offspring. He uses a "watch and learn" system— a more 'organic' learning method that strengthens each child's independance and self-teaching curiousity.
Oberon's Reason: shadow. Infinite shadow must be explored, it is the single most powerful difference between the Courts and Amber. It is the Pattern's single most important mechanism, and Amber's greatest weapon of knowledge, learning, defense, and influence: Shadow. This cultural contrast is the point of departure.
The royals of Amber with the "encyclopeadia of Shadow" before them as a playground and school of hard knocks; versus the Courts of Chaos with the vast experience of towering over every civilization that has ever gone before.
The Courts are the successful conquerors of all external threats. In Chaos, internal foes and competitors are the greatest challenge and this leads to secrecy and perfect execution of manipulating strategies. I'll paraphrase myself from comments about 'Bloody Grievance':
. . . the cultural clash, aggravated by common language of Thari, is amplified by the amazing longevity and success of the Courts of Chaos. The very extraordinary success of the Courts against the poor "dweebs" of shadow has ill-prepared the Chaos Lords for the kind of contest that is staged in 'Bloody Grievance'.
Post-game, we used the American colonials and British Empire example for the battles fought in this first contest between Chaos and Amber.
But this culture clash only sets the stage. I decided I wanted to amplify the differences. I wanted to rely less on the odd sensations of whirling madness that Corwin describes in Chaos, and get to an appealing separation between the Chaos folks that carve out an Empire, and the folks that eventually polish the vitality right out of it.
So part of my "alien" Chaos pivots around the axis of time-dilation with respect to Amber, which gets progressively worse as the centuries roll by. Chaos is moving both faster and slower than Amber, to a rhythm that is unpredictable. What I mean is that while I might model modern Chaos on a very traditional (rather Imperial) mindset, with plenty of social controls for Elders to consolidate power against enterprising youngers, the fact is that Dworkin and Oberon left this Chaos a very long time ago. The Chaos of their origin and formation has changed in the intervening time to something more refined, more sophisticated, more alien to the primitive "carve an empire" attitudes of Dworkin and Oberon, and to smaller degree, Oberon's kids.
I use time dilation to effect dramatic difference between the way Chaos thinks today and the way they thought in Dworkin's day. Taken to an extreme, Chaos is so successful it has stopped learning new things. The culture is gaining nothing new and they believe their own success demonstrates that they have all the answers they need. Yes, they are masters of subtrefuge and manipulation, but this is in the face of other masters of subtlety and connivance. Against a brutal opponent, or a street-wise one, or a shadow-broadened one, they might be a bit less prepared. They might be shocked right out of their smug safe perfection. They might even fall flat on their faces. And later (second series), the young and ambitious traditionalists of Chaos might make a cult of the aggressive and vibrant Amberites.
OK. So how the heck does this play out in a game? Well, in a campaign, you have time to model alien characters who think differently, who act in ways you (as Players) think you understand, only to find out later that you didn't.
In a con game, you don't have the same time or tools to impress the weirdness factor on the Players. So again, I go for dramatic impact and worry less about subtle canon. I imagined the clever but rigid system of the Japanese feudal lords (Chaos) meeting the street-wise tough guys of Raymond Chandler (Amber, as written by Zelazny). But each side has the same base language, similar appearance, and this allows them to completely misunderstand each other, which the GM takes to extremes at every opportunity of the common language. So elements that I contrasted and emphasized were:
In one game, the amber spokesperson mentioned having to "fetch Oberon" to be present at the next meeting. The GM pounced on this: the Chaosian spokesperson was then quite alarmed that a "fetch" of Oberon was going to be used in serious ceremonies, and what did the amberite mean by suggesting that these matters were not important enough to have the real Oberon present?
Of course, the Chaosian's actual reply was subtle, not obvious, and the source of the misunderstanding about the two words was never worked out.
The Chaosians felt they were being tested and toyed with in order to break their control of form and the confrontation. Of course, the Amberites were just as paranoid from a survival perspective.
Language, appearance, the devil in the details, all based off of the Players input. Add in the rituals, the slightly cthonic armor, the pageantry, strange-eyed pale-faced people of blank expression, and you can overwhelm the moment. It's a pretty effective combo for putting the Players on constant watch.